I guess I'm just having trouble visualizing why my stitches wouldn't "fit" on a 24" cable if they fit on the shorter 16" cable. Maybe I'll have to just experiment a little first with some leftover yarn so that I can actually see what the problem is ... I've always been a visual learner!

Think about the circumferance of the hat...
An adult hat will run you somewheres between 22" and 24". Your stitches may "fit" on the 24" but even if you stretched the knitting out as far as it will go, you wont have enough inches in stitches to actually work the thing.

So if you dont have enough stitches to go around the needle comfortably, you should go with a shorter needle.

Does that help a little more?

__________________"Be who you are and say what you feel because
those who mind don't matter and those who matter don't mind." - Dr. Seuss

You don't need a 16", you can use the 24" needle with the single loop version of magic loop. I use it for hats all the time. If you inc sts after the cuff, you won't need to loop it again until you do the decs as the sts should fit around it.